> No, the challenge can be posed in a way that refers to an arbitrary agent
> A which a constant challenge C accepts as input.

But the problem with saying it this way, is that the "constant challenge"
has to have an infinite memory capacity.

So in a sense, it's an infinite constant ;)

> No, the charm of the physical challenge is exactly that there exists a
> physically constant cavern which defeats any AIXI-tl that walks into it,
> while being tractable for wandering tl-Corbins.

No, this isn't quite right.

If the cavern is physically constant, then there must be an upper limit to
the t and l for which it can clone AIXItl's.

If the cavern has N bits (assuming a bitistic reduction of physics, for
simplicity ;), then it can't clone an AIXItl where t >>2^N, can it?  Not
without grabbing bits (particles or whatever) from the outside universe to
carry out the cloning.  (and how could the AIXItl with t>>2^N even fit
inside it??)

You still need the quantifiers reversed: for any AIXI-tl, there is a cavern
posing a challenge that defeats it...

> > I think part of what you're saying here is that AIXItl's are
> not designed to
> > be able to participate in a community of equals....  This is
> certainly true.
> Well, yes, as a special case of AIXI-tl's being unable to carry out
> reasoning where their internal processes are correlated with the
> environment.


(See, it IS actually possible to convince me of something, when it's
correct; I'm actually not *hopelessly* stubborn ;)


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